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## Problem Description

Gug is having fun with barcodes! A barcode is a string of 0s and 1s. Gug will only be happy if the 1s in the barcode can be divided into consecutive sections of length *X* to *Y*. Note that 2 consecutive sections of 1 do not need to be divided by a 0 in between.

Gug is able to edit the barcode by changing 0 to 1 or 1 to 0 at chosen position(s) in the barcode. Given a barcode of length *N*, find the minimum operations it takes for Gug to be happy.

## Input

The first line of input will contain a 3 integers, *N*, *X*, *Y*.

The second line of input will contain a string of length *N*, representing the barcode.

## Output

The output should contain one integer representing the minimum number of operations it takes for Gug to be happy if he starts with the given barcode.

## Limits

Subtask 1 (30%): 1 ≤ N ≤ 10^{3}, 0 ≤ X, Y ≤ N.

Subtask 2 (31%): 1 ≤ N ≤ 10^{5}, 0 ≤ X = Y ≤ N.

Subtask 3 (39%): 1 ≤ N ≤ 10^{5}, 0 ≤ X, Y ≤ N.

Subtask 4 (0%): Sample Testcases.

## Sample Input 1

8 3 4 01010101

## Sample Output 1

2

## Explanation

Gug changes the barcode from 01010101 to 01110111, taking 2 operations.## Sample Input 1

8 4 5 10001010

## Sample Output 1

3

## Explanation

Gug changes the barcode from 10001010 to 00001111, taking 3 operations.### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 30 | 20 | 1s | 256MB | Minimum |

2 | 31 | 20 | 1s | 256MB | Minimum |

3 | 39 | 60 | 1s | 256MB | Minimum |

4 | 0 | 2 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o barcode -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512